A geologist in South America discovers a bird skeleton that contains 43% of its original amount of C-14. K value
of C-14 is 0.0001
Find the age of the bird skeleton to the nearest year.

1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,

[tex]x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}[/tex]

This means that the length of the hypotenuse is:

[tex]\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}[/tex]

2) (Diagram attached) We know that

[tex]\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}[/tex]  (in cm)

3) From the Pythagorean identity,

[tex]\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}[/tex]

4) [tex]\frac{\pi}{6}[/tex]

Answer:

2j + 8

Step-by-step explanation:

Given:  8 more than twice Jenny's age

Let j = Jenny's age

"twice Jenny's age" means double (multiply by 2) Jenny's age  = 2j

"more than" means to add, so "8 more than" = + 8

Therefore:

"8 more than twice Jenny's age" = 2j + 8

Answer:

B. 3.25 p.m.

Step-by-step explanation:

[tex]20 + 30 + 45 = 96 \: minutes \\ 95 \: minutes \: = 60 \: minutes + 35 \: minutes \\ 95 \: minutes \: = 1 \: hour \: 35 \: minutes\\ 5.00 \: p.m. - 1 \: hour \: 35 \: minutes = 3.25 \: p.m.[/tex]

Answer:

Y=-58

Step-by-step explanation:

Y=-2(3)^(2)-4

Y=-2(3*3*3)-4

Y=-2(27)-4

Y=-54-4

Y=-58

Answer:

B

Step-by-step explanation:

On edge

Answer:

11.625 or mixed number form 11 [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

divide 46.5 by 4

Answer:

If you mean 656, then the answer is 509,712.

Edit: If you're talking about measurements, then it would be 50,893 feet and 6 inches.

Answer:

$90,000

Step-by-step explanation:

We can can use substitution for this. First, we need to create two separate problems that represent this situation. The house and the lot together cost 120000, so we can make the equation h+l=120000. We also know that the house is worth 3 lots, so we can make the equation h=3l. Because h=3l, we can substitute for h, making the equation 3l+l=120000, or 4l=120000. To isolate l, we have to divide both sides by 4. If we do that, we get l=30000. Now, we have to substitute to find h. Our new equation is h+30000=120000. To isolate h, we have to subtract 30000 from each side. If we do this, we get h=90000. That's our answer.

Hope this helps!

The expression is equal to 3sqrt(517)/5

Answer:

A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]

Step-by-step explanation:

For this problem, we have to combine like terms.

Let's look at the equation:

[tex](12x^{4} -4x^{3} +7x+6)+(3x^{2} -4x+14)[/tex]

[tex]12x^{4[/tex], [tex]-4x^{3}[/tex], [tex]3x^{2}[/tex] do not have any other like terms, so we keep all in the final answer.

[tex]7x[/tex] and [tex]-4x[/tex] are like terms, so we combine them. [tex]7x-4x=3x[/tex]

14 and 6 are like terms, so we combine them. 14+6 = 20

Let's put everything into the final equation:

[tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]

So, the final answer is A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]

Hope this helps! If you have any questions about my work, leave them in the comments below!

[tex]y = -x^2+10x\implies y = -x^2+10x+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 10}{2(-1)}~~~~ ,~~~~ 0-\cfrac{ (10)^2}{4(-1)}\right)\implies \left( \cfrac{10}{2}~~,~~\cfrac{100}{4} \right)\implies (5~~,~~25)[/tex]

Answer:

[tex]y^{12} + b^{8} \\OR\\12y + 8b[/tex]

Step-by-step explanation:

If the statement is  

[tex]y^{12} + b^{16-8} \\y^{12} + b^{8} \\[/tex]this can't be more simplified

If the statement is

[tex]y{12} + b{16-8} \\y{12} + b{8} \\\\rearrange\\12y + 8b[/tex]

Answer:

the next sequence is 76+19= 95

Answer:

Next number = 95

Step-by-step explanation:

Hi! Let me help you out.

_________________

To determine the next number in this sequence, we should determine the common difference.

We can do it like this.

[tex]\longmapsto\sf 76-57=19[/tex]

See. I took the third term, and subtracted the second term from it.

Continue.

[tex]\longmapsto\sf 57-38=19[/tex]

                                              ↪

The number we obtain after subtracting is the common difference.

So we should take the third term, "76", and add the common difference, "19" to it.

We obtain 95. Which is the final answer.

⇨Hope that this helped you out! have a great day ahead.⇦

Best Wishes!

[tex]\star\bigstar\overline{\textsf{Reach far. Aim high. Dream big.}}[/tex]

◆◈-Greetings!-◈◆

_______________

Step-by-step explanation:

4(y+8)=9

for this sum first we need to multiply 4to y and 4 to 8

4y+32=9

then u need to -9 from both sides

4y=23

y=23/4

u will get the answer

Answer:

X=4

Step-by-step explanation:

Eveything is explained in the pic. Hope that helps ;)

Answer:

R s. 36

Step-by-step explanation:

1kg ⇒ 1000g

So, a quarter kilogram means,

[tex]\frac{1}{4}[/tex] × 1kg = 1000g ×  [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{4}[/tex] × 1kg = 250g

According to the question,

250g = R s. 60

So, now they're asking for the price of 150g.

Let that price be x.

250g ⇒ R s. 60

150g  ⇒ x

Use cross multiplication to find the value of x.

250x = 60 × 150

250x = 9000

Divide both sides by 250.

x = R s. 36

Answer: An even number between 7 and 16 would be 10.

Step-by-step explanation: I am not sure how I am supposed to draw a picture of the number other than drawing the number itself. However, 10 is an even number because it is a composite number and is divisible by 2. 10 is an even number, not an odd number. Hope this helps!

Answers.

The instructional activity to explain the conversion will be:

The lessons should include:

Learn more about instructional activity on:

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The value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a right angle triangle shown in the picture.

We can use SOHCAHTOA to find the unknown length.

Using the ratio of tan which is opposite to adjacent (TOA)

tan8 = 9/n

n = 64.038 ≈ 64.04

Thus, the value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)

Learn more about trigonometry here:

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Answer:

A=3

B=31

Step-by-step explanation:

A)5-2=3

b)

17-10=7

10-5=5

7-5=2

2×7=14

14+17=31

The length of ribbon C is  37 feet.

The equation that can be used to determine the length of ribbon C is:

C = 34 + ( length of ribbon B - length of ribbon A)

C = 34 + (59 - 56)

C = 34 + 3

c = 37 feet

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The vertex of the graph moves to a point twice as far from the y-axis.

Option B is the right answer.

The general equation of a parabola is

y = a(x-h)² + k

or

x = a(y-k)² +h

where (h,k) denotes the vertex.

It is given in the question that the value of h is doubled for the equation given

y = a(x-h)² + k

if the value of the h is doubled, the vertex of the graph shifts and shifts on the x axis away from the y axis , therefore

the vertex of the graph moves to a point twice as far from the y-axis.

Option B is the right answer.

To know more about Parabola Equation

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Answer:

its b

Step-by-step explanation:

Answer:

The symbol is a variable called x, which is a mathematical term used to substitute values in mostly linear and quadratic equations.

Answer:

a term.

Step-by-step explanation:

(I'm assuming you're asking about the underlined,)

therefore the 9x is a term

(top line)

the 9 is a coefficient

the x is a variable

5 is a constant

- (subtraction sign) is the operator.

9x - 5 is an expression

(bottom line)

the 3x is also a term

x is the variable

3 is a coefficient

4 is the constant

the + (addition sign) is the operator

3x + 4 is the expression.

the answer would be a constant and a term

hope this helps:)

Answer:

7/11

Step-by-step explanation:

blue = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7 that will be blue.

green = 1 + 1 + 1 + 1 = 4 that will be green.

So it’s going to be 7 + 4 = 11 in total then do

7/11

Is it 7/22

Answer:

Step-by-step explanation:

(4x³)² (3x)⁵ = 4²(x³)² (3)⁵(x)⁵

                 = 16x⁶ (243)x⁵

                 = (16 × 243) (x⁶ × x⁵)  [commutative property]

                 = (3888) (x¹¹)   [exponent property]

                 = 3888x¹¹